Saw dust isn't an ideal fibrous material, but it's still primarily composed of fibers [see 1]. Really they're a bundle of fibers. On a macro scale it makes less sense, but on a micro-scale the fibers are much longer than the micro-cracks that begin to form in materials under strain and which lead to the loss of strength or fracture we normally think about.

1: https://www.sciencedirect.com/science/article/pii/B978012814...